Let us consider the total number of relativistic degrees of freedom $g(T)$ for particle species in our universe:
$$g(T)=\left(\sum_Bg_B\right)+\frac{7}{8}\left(\sum_Fg_F\right)$$
Where the sums are ...

What if in the experiment by Veritasium Bullet Block Explained, we used an ideal block and bullet, so that the collision is perfect elastic, and the bullet doesn't stick to the block after hitting it? ...

While doing some calculation in Statistical Mechanics of blackbody radiation from Huang's Statistical mechanics, I came across with the factor 2 which it says comes from two possible polarizations. ...

It is sometimes stated that any classical underpinnings (rightly non-local) of a general quantum system are unrealistic or unphysical because these require exponentially more information to store what ...

If people are talking about 4 or higher dimensions they are always pictured as space dimensions. But if you have have a look at the simplest definition of a mathematical dimension it only needs to be ...

Massless vector bosons have only two independent degrees of freedom, while massive ones have three. In spontaneous symmetry breaking, the massless vector belonging to the broken group becomes massive ...

In his lectures professor Hamber said that the metric tensor is not unique, just like the 4 vector potential is not unique for a unique field in electrodynamics. Since the metric tensor is symmetric, ...

In classical physics, we have second-order equations like Newton's laws, so we need to specify both position (zeroth order) and velocity (first order) of a particle as initial conditions, in order to ...

How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that
involves the ...

I'm learning about constraints and I know the following: If there are $N$ particles in 3 dimensional space, I have $3N$ degrees of freedom. If I have $n_b$ holonomic constraints and I switch over to ...

The $\mathrm{U(1)}$ QED case has two physical degrees of freedom, which is easy to understand because the free electromagnetic field must be transverse to the direction of propagation. But what are ...

It it known that the massive spin-2 irreducible representation of the Poincare group is the traceless symmetrical transverse 4-tensor $h_{\mu \nu}$ with rank 2:
$$
(\partial^{2} + m^{2})h_{\mu \nu} = ...

I understand how, if the Riemann tensor is 0 in all its components, since we construct the Ricci tensor by contracting the Riemann, Ricci tensor would be 0 in all components as well.
I've read that ...

The EM field has two possible polarizations, which is caused by spin-one nature of field (leads to the Lorenz gauge) and massless of the field. Really, the Klein-Gordon equations for the EM field
$$
...

I clearly am interpreting the Virial Theorem incorrectly, but I don't know how. In dipole gases, the molecules can exhibit five kinetic modes, while they can only experience 2 potential modes. Doesn't ...

Today, my friend (@Will) posed a very intriguing question -
Consider a complex scalar field theory with a $U(1)$ gauge field $(A_\mu, \phi, \phi^*)$. The idea of gauge freedom is that two solutions ...

Sean Carroll has a new popularization about the Higgs, The Particle at the End of the Universe. Carroll is a relativist, and I enjoyed seeing how he presented the four forces of nature synoptically, ...